Advertisements
Advertisements
Question
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
Options
Rajesh did not live in Bangalore or Rajni lives in Bangalore
Rajesh lives in Bangalore and Rajni did not live in Bangalore
Rajesh did not live in Bangalore and Rajni did not live in Bangalore
Rajesh did not live in Bangalore or Rajni did not live in Bangalore
Advertisements
Solution
The negation of the statement “Rajesh or Rajni lived in Bangalore” is rajesh did not live in Bangalore and Rajni did not live in Bangalore.
Explanation:
Let p: Rajesh or Rajni lives in Bengaluru
And q: Rajesh lived in Bengaluru
r: Rajni lived in Bengaluru
~ q: Rajesh did not live in Bengaluru
~ r: Rajni did not live in Bengaluru
∴ ~ (q ∨ r) = (~ q ∧ ~ r): Rajesh did not live in Bengaluru and Rajni did not live in Bengaluru.
APPEARS IN
RELATED QUESTIONS
By giving a counter example, show that the following statements are not true.
p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
Find out the sentence are statement and are not. Justify your answer.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
Go !
Give three examples of sentences which are not statements. Give reasons for the answers.
I will not go to school.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
To apply for a driving licence, you should have a ration card or a passport.
Write of the statement in the form "if p, then q".
You can access the website only if you pay a subscription fee.
Write of the statement in the form "if p, then q".
There is traffic jam whenever it rains.
Write of the statement in the form "if p, then q".
It is necessary to be rich in order to be happy.
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
statement are true and false? In each case give a valid reason for saying so
q : The centre of a circle bisects each chord of the circle.
Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Which of the following statements are compound statements
“Ram and Rahim are friends”
Rewrite the following statements in the form of conditional statements:
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
A triangle has three sides.
Find the component statements of the following compound statements.
Number 7 is prime and odd.
Find the component statements of the following compound statements.
Chennai is in India and is the capital of Tamil Nadu.
Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.
Find the component statements of the following compound statements.
Chandigarh is the capital of Haryana and U.P.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
35 is a prime number or a composite number
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
Rewrite the following statements in the form of conditional statements
You will fail, if you will not study.
Identify the Quantifiers in the following statements.
For all negative integers x, x 3 is also a negative integers.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
Which of the following is not a statement>
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
